The growth of epitaxial (001)-oriented SrBi2Ta2O9 thin films by pulsed laser deposition (PLD) has been investigated. The effects of target composition, substrate temperature, oxidant pressure, laser pulse rate, laser fluence, and sample cooling have been studied. Variation of deposition parameters significantly affects the phase purity and epitaxial perfection of these ferroelectrics, and individual and combinatorial effects of the aforementioned growth variables as related to the adsorption-controlled growth regime are discussed. X-Ray diffraction and Rutherford backscattering spectrometry (chi (min) = 12%) analyses indicate that the (001)-oriented epitaxial films grown under the optimized conditions identified in this study have the highest structural perfection reported to date.